Debra Boutin and Sally Cockburn, respectively the Samuel F. Pratt and the William R. Kenan, Jr. Professors of Mathematics, published a chapter titled 'Symmetry Parameters for Mycielskian Graphs' in the book Research Trends in Graph Theory and Applications, Springer, 2021.
Their chapter was a joint work with Lauren Keough from Grand Valley State University, Sarah Loeb from Hampden-Sydney College, K. E. Perry from the University of America, and Puck Rombach from the University of Vermont.
The book volume is the result of research begun at a five-day workshop at the Institute for Mathematics and Its Applications at the University of Minnesota in August 2019. Each team of six or seven researchers pursued a different topic, and each team contributed a related chapter to this volume.
A Mycielskian graph is the result of extending an original graph, much like a skyscraper extends a ground floor plan. In their chapter, the authors cover a number of symmetry parameters of a Mycielskian graph in terms of symmetry parameters for the original graph. The symmetry parameters studied include: determining number, distinguishing number, and the cost of 2-distinguishing.